Solenoids And Toroids

Step 1: Understanding the Concept:
A solenoid is a coil of wire that produces a nearly uniform magnetic field in its interior when a current is passed through it. The strength of this magnetic field depends on the number of turns per unit length, the current, and the permeability of the medium inside.

Step 2: Key Formula or Approach:
The magnitude of the magnetic field inside a long solenoid is given by the formula: where is the permeability of free space ( ), is the current, and is the number of turns per unit length. The number of turns per unit length is calculated as , where is the total number of turns and is the length of the solenoid.

Step 3: Detailed Explanation:
Given data:
Length of the solenoid, .
Total number of turns, .
Current, .
Calculation:
First, calculate the number of turns per unit length, : Now, substitute the values into the magnetic field formula: Now, we calculate the numerical value using : This is equal to 20.106 mT. The closest option is 20 mT.

Step 4: Final Answer:
The magnitude of the magnetic field inside the solenoid is approximately 20 mT.